A103604 a(n) = C(n+6,6) * C(n+10,6).

210, 3234, 25872, 144144, 630630, 2312310, 7399392, 21237216, 55747692, 135795660, 310390080, 671571264, 1385115732, 2738894004, 5216940960, 9610154400, 17178150990, 29881321470, 50707697040, 84126042000, 136704818250, 217946538810, 341398774080, 526116951360

Offset

0,1

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Formula

G.f.: -42*(5*x^2+12*x+5) / (x-1)^13. - Colin Barker, Jul 01 2015

a(n) = A000579(n+6)*A000579(n+10). - Michel Marcus, Jul 01 2015

From Amiram Eldar, Sep 06 2022: (Start)

Sum_{n>=0} 1/a(n) = 60*Pi^2 - 10445899/17640.

Sum_{n>=0} (-1)^n/a(n) = 447173/2205 - 2048*log(2)/7. (End)

Mathematica

Table[Binomial[n+6, 6]Binomial[n+10, 6], {n, 0, 30}] (* or *) LinearRecurrence[ {13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1}, {210, 3234, 25872, 144144, 630630, 2312310, 7399392, 21237216, 55747692, 135795660, 310390080, 671571264, 1385115732}, 30] (* Harvey P. Dale, Apr 18 2019 *)

Prog

(PARI) a(n) = binomial(n+6, 6)*binomial(n+10, 6) \\ Colin Barker, Jul 01 2015
(PARI) Vec(-42*(5*x^2+12*x+5)/(x-1)^13 + O(x^30)) \\ Colin Barker, Jul 01 2015

Crossrefs

Cf. A000579.

Sequence in context: A027822 A024449 A235240 * A257711 A061133 A087977

Adjacent sequences: A103601 A103602 A103603 * A103605 A103606 A103607

Keyword

nonn,easy

Author

Zerinvary Lajos, Apr 22 2005

Status

approved